📚 Practical Case Study Exercises in Statistics for Year 9 OCR | Year 9 OCR 统计：案例分析实战演练
Statistics is not just about numbers and formulas – it is about making sense of the world. In this article, we will work through several realistic case studies that a Year 9 student following the OCR curriculum might encounter. Each case study will guide you through the complete statistical enquiry cycle: posing a question, collecting data, presenting data, analysing results, and drawing conclusions. You will gain hands-on practice with bar charts, pie charts, scatter graphs, averages, measures of spread, and basic probability. Whether you are preparing for an assessment or simply want to strengthen your data-handling skills, these examples will help you think like a statistician.
统计学不仅仅是数字和公式——它关乎于理解世界。在这篇文章中，我们将演练几个符合 OCR 课程体系的、九年级学生可能会遇到的真实案例研究。每个案例都会带你走完完整的统计调查循环：提出问题、收集数据、展示数据、分析结果并得出结论。你将亲手实践条形图、饼图、散点图、平均数、分布度量以及基础概率。无论你是在准备考试还是只想强化数据处理技能，这些例子都会帮助你像统计学家一样思考。
1. Case Study Overview: The Statistical Enquiry Cycle | 案例总览：统计调查循环
Every real-world statistics problem follows a structured process known as the statistical enquiry cycle. For OCR Year 9, the key stages are: (1) Plan – decide on a hypothesis or research question; (2) Collect – gather primary or secondary data; (3) Process and present – organise data using tables and graphs; (4) Analyse – calculate averages, spread, and look for patterns; (5) Evaluate – reflect on limitations and reliability. Our case studies will follow these steps so you can see how each one links together.
每一道真实世界的统计问题都遵循一个被称为统计调查循环的结构化过程。对于 OCR 九年级来说，关键步骤是：(1) 计划——确定假设或研究问题；(2) 收集——收集一手或二手数据；(3) 处理与展示——用表格和图表整理数据；(4) 分析——计算平均数、分布范围并寻找规律；(5) 评价——反思局限性和可靠性。我们的案例分析将按照这些步骤进行，以便你看到它们是如何串联起来的。
2. Case Study 1: Screen Time and Sleep – Planning a Survey | 案例一：屏幕时间与睡眠——设计调查
A group of Year 9 students wonder: 'Does the amount of screen time before bed affect how many hours of sleep we get?' They plan to ask classmates to record, for one week, their daily screen time in the hour before bed and their total sleep duration. The hypothesis is: the more evening screen time, the less sleep. This is a primary data collection plan using a diary method, and it produces bivariate continuous data ready for a scatter graph.
一群九年级学生想知道：“睡前看屏幕的时间会影响我们的睡眠时长吗？”他们计划请同班同学在一周内记录每天睡前1小时的屏幕时间以及总睡眠时长。假设是：晚间屏幕时间越长，睡眠越少。这是一个使用日记法收集一手数据的计划，将产生适用于散点图的双变量连续数据。
3. Case Study 1: Data Collection and Organisation | 案例一：数据收集与整理
The students collected data from 30 classmates. After removing any incomplete entries, they had 28 pairs of data. They summarised the raw data in a frequency table grouped by screen time: 0–15 min, 16–30 min, 31–45 min, 46–60 min. For each group, they listed corresponding sleep times. To protect privacy, they used anonymous codes like Student01. The data is now ready for graphing.
学生们从30位同学那里收集了数据。剔除不完整记录后，得到28组成对数据。他们将原始数据按屏幕时间分组汇总成频数表：0–15分钟、16–30分钟、31–45分钟、46–60分钟。每个组都列出了对应的睡眠时长。为了保护隐私，他们使用了如Student01的匿名代码。数据现已准备好进行绘图。
4. Case Study 1: Presenting Data on a Scatter Graph | 案例一：用散点图展示数据
A scatter graph is the best choice for displaying the relationship between two continuous variables. Each point on the graph represents one student, with screen time (minutes) on the x-axis and sleep (hours) on the y-axis. The plotted points show a general downward trend: as screen time increases, sleep tends to decrease. A line of best fit can be drawn to model the relationship and make predictions, such as estimating sleep for 50 minutes of screen time.
散点图是展示两个连续变量之间关系的最佳选择。图上的每个点代表一名学生，x轴为屏幕时间（分钟），y轴为睡眠时长（小时）。绘制的点呈现出总体下降趋势：屏幕时间增加，睡眠往往减少。可以画一条最佳拟合线来模拟这种关系并进行预测，比如估计屏幕时间为50分钟时的睡眠时长。
5. Case Study 1: Analysing with Averages and Correlation | 案例一：用平均数和相关性进行分析
The students calculated the mean screen time as 38 minutes and mean sleep as 7.2 hours. However, the mean hides individual variation. They described correlation: the scatter graph shows a moderate negative correlation. They did not have a calculator to compute the exact correlation coefficient, so they used visual interpretation. It is important to note that correlation does not mean causation – other factors like stress or caffeine could also affect sleep.
学生们计算出平均屏幕时间为38分钟，平均睡眠为7.2小时。然而，平均数掩盖了个体差异。他们描述了相关性：散点图显示出中等程度的负相关。由于没有计算器来算出准确的相关系数，他们采用了目测解读。需要注意的是，相关性并不意味着因果关系——如压力或咖啡因等其他因素也可能影响睡眠。
6. Case Study 2: Favourite Leisure Activities – Categorical Data | 案例二：最喜爱的课外活动——类别数据
Another class wanted to know how Year 9 students prefer to spend their free time. They designed a simple questionnaire offering five options: Sports, Reading, Gaming, Music, and Social Media. They surveyed 120 students chosen at random from the year group. The data collected is categorical (qualitative), and the most suitable diagrams are bar charts or pie charts. They also recorded whether each respondent was male or female to allow comparison by gender.
另一个班级想知道九年级学生最喜欢如何度过空闲时间。他们设计了一份简单的问卷，提供五个选项：运动、阅读、游戏、音乐和社交媒体。他们从年级中随机抽取了120名学生进行调查。收集到的数据是类别（定性）数据，最适合的图表是条形图或饼图。他们还记录了每位受访者是男性还是女性，以便按性别进行比较。
7. Case Study 2: Creating and Interpreting a Bar Chart | 案例二：制作与解读条形图
The data was summarised in a two-way table. Frequencies were: Sports (24), Reading (18), Gaming (30), Music (22), Social Media (26). The students drew a dual bar chart to compare males and females. The chart revealed that Gaming was far more popular among boys, while Social Media and Reading had higher frequencies for girls. Bars must be labelled clearly, with axes showing category and frequency, and a key for male/female.
数据汇总在一个双向表中。频数为：运动(24)、阅读(18)、游戏(30)、音乐(22)、社交媒体(26)。学生们绘制了双重条形图来比较男生和女生。图表显示，游戏在男生中受欢迎得多，而社交媒体和阅读在女生中频数更高。条形必须清晰标记，轴要显示类别和频数，并附有男/女的图例。
8. Case Study 2: Using a Pie Chart and Mode | 案例二：使用饼图与众数
mode (most frequent category) was Gaming. Pie charts are excellent for seeing relative shares, but do not show exact frequencies as easily as a bar chart. Students discussed whether the mode gave a full picture, noting that with only 120 students, the difference between Gaming (30) and Social Media (26) is small.
还绘制了饼图来显示选择每项活动的学生所占的比例。游戏的扇形为90°，因为(30/120)×360 = 90°。众数（最常见的类别）是游戏。饼图非常适合查看相对份额，但不如条形图那样容易显示确切频数。学生们讨论了众数是否能反映全貌，并指出在只有120名学生的情况下，游戏(30)和社交媒体(26)之间的差距很小。
9. Case Study 3: Reaction Times – Comparing Two Groups | 案例三：反应时间——比较两组
A science teacher asked students to test whether listening to music affects reaction time. Students measured the time (in milliseconds) it took to catch a dropped ruler under two conditions: silent and with music. Each student contributed two reaction times. This is a paired data collection. The aim is to compare the central tendency and spread of the two sets. The data is continuous, so histograms or box plots could be used, but for Year 9, comparative dot plots and mean/median are appropriate.
一位科学老师让学生测试听音乐是否会影响反应时间。学生们测量了在安静和听音乐两种条件下接住下落尺子所需的时间（以毫秒为单位）。每个学生提供了两个反应时间。这是一个配对数据收集。目标是比较两组数据的集中趋势和分布范围。数据是连续的，因此可以使用直方图或箱线图，但对于九年级来说，比较性的点图和平均数/中位数是合适的。
10. Case Study 3: Mean, Median, and Range Comparison | 案例三：平均数、中位数和极差的比较
For the silent condition, the mean reaction time was 215 ms, median 210 ms, range 85 ms. For the music condition, the mean was 248 ms, median 240 ms, range 120 ms. The music condition had both a higher average and a larger spread. The median is less affected by extreme values, so it confirms the shift. The range suggests more variation when music is playing, possibly because some students are distracted more than others.
在安静条件下，平均反应时间为215毫秒，中位数为210毫秒，极差为85毫秒。在音乐条件下，平均值为248毫秒，中位数为240毫秒，极差为120毫秒。音乐条件下的平均值更高且分布更广。中位数受极端值影响较小，因此它证实了这种变化。极差表明在播放音乐时变异性更大，可能是因为有些学生比其他人更容易分心。
11. Case Study 3: Drawing Conclusions and Evaluating the Method | 案例三：得出结论与评价方法
The students concluded that listening to music increases reaction time on average by about 30 ms, suggesting a slight decrease in concentration. However, they identified several limitations: sample size was only 20 students; the ruler-drop test can be inaccurate; the type and volume of music were not controlled; and practice effects might influence the second trial. They suggested a larger sample and randomising the order of conditions for future investigations.
学生们得出结论，听音乐平均使反应时间增加了约30毫秒，这表明注意力略有下降。然而，他们发现了几个局限性：样本量仅为20名学生；尺子下落测试可能不准确；音乐的类型和音量未受控制；练习效应可能影响第二次试验。他们建议未来研究应使用更大的样本并将条件顺序随机化。
12. Case Study 4: Probability from a Spinner Experiment | 案例四：转盘实验中的概率
To explore probability, students made a spinner with four colours: red, blue, green, and yellow. They said the spinner was fair (equal sections). They spun it 100 times and recorded the results: Red 22, Blue 31, Green 24, Yellow 23. They compared experimental probabilities (relative frequencies) with theoretical probability (0.25 for each colour). The experimental probabilities were Red 0.22, Blue 0.31, Green 0.24, Yellow 0.23. They used a bar chart to visualise the differences.
为了探索概率，学生们制作了一个有四种颜色的转盘：红、蓝、绿、黄。他们称转盘是公平的（各区域相等）。他们转动了100次并记录结果：红色22次，蓝色31次，绿色24次，黄色23次。他们将实验概率（相对频数）与理论概率（每种颜色0.25）进行了比较。实验概率为红色0.22，蓝色0.31，绿色0.24，黄色0.23。他们用条形图展示了这些差异。
13. Case Study 4: Understanding Variation and Sample Size | 案例四：理解变异性和样本量
Blue occurred more often than expected. Is the spinner biased? the number of spins to 500, the experimental probabilities would likely get closer to 0.25 – giving 0.76, close to the theoretical 0.75. This shows that simple events can be combined.
蓝色出现的次数多于预期。这个转盘有偏倚吗？不一定。在只有100次转动的情况下，变异是正常的。他们讨论到，如果将转动次数增加到500次，实验概率可能会更接近0.25——这就是大数定律。他们还计算了转到原色（红+蓝+黄）的概率为22+31+23 = 76次，占100次中的0.76，接近理论值0.75。这表明简单事件可以组合。
14. Bringing It All Together: Skills for OCR Year 9 Statistics | 融会贯通：OCR 九年级统计技能
Through these case studies, you have practised planning a statistical enquiry, collecting and organising raw data, choosing the right graph (bar chart, pie chart, scatter graph, dot plot), calculating mean, median, mode, and range, interpreting correlation, and using experimental probability. OCR Year 9 statistics assessments often ask you to critique data collection methods or suggest improvements, so always think about sample size, bias, and fairness. The more you engage with real data, the more confident you become.
通过这些案例研究，你练习了规划统计调查、收集和整理原始数据、选择正确的图表（条形图、饼图、散点图、点图）、计算平均数、中位数、众数和极差、解读相关性以及使用实验概率。OCR 九年级统计评估经常会要求你评判数据收集方法或提出改进建议，因此要始终考虑样本量、偏倚和公平性。你接触的真实数据越多，你就越自信。
Published by TutorHao | Statistics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图